Try the Registry of Deeds records in PRONI, Belfast. You can search under the name William Ardrey, or if you know the exact townland where he had the property, you can also search under townland. (Pomeroy itself is not a townland).
Bear in mind that only about 10% of the population owned land. The rest rented and when they spoke of selling up a farm etc, what they really meant was that they were selling the unexpired portion of a lease. However if the lease was for over 3 years it might be recorded in the Registry of Deeds.